On Verification of Restricted Extended Affine Equivalence of Vectorial Boolean Functions

Conference paper

DOI: 10.1007/978-3-319-16277-5_8

Volume 9061 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Özbudak F., Sınak A., Yayla O. (2015) On Verification of Restricted Extended Affine Equivalence of Vectorial Boolean Functions. In: Koç Ç., Mesnager S., Savaş E. (eds) Arithmetic of Finite Fields. WAIFI 2014. Lecture Notes in Computer Science, vol 9061. Springer, Cham

Abstract

Vectorial Boolean functions are used as substitution boxes in cryptosystems. Designing inequivalent functions resistant to known attacks is one of the challenges in cryptography. In doing this, finding a fast technique for determining whether two given functions are equivalent is a significant problem. A special class of the equivalence called restricted extended affine (REA) equivalence is studied in this paper. We update the verification procedures of the REA-equivalence types given in the recent work of Budaghyan and Kazymyrov (2012). In particular, we solve the system of linear equations simultaneously in the verification procedures to get better complexity. We also present the explicit number of operations of the verification procedures of these REA-equivalence types. Moreover, we construct two new REA-equivalence types and present the verification procedures of these types with their complexities.

Keywords

Vectorial Boolean functions EA-equivalence REA-equivalence 

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of MathematicsMiddle East Technical UniversityAnkaraTurkey
  2. 2.Institute of Applied MathematicsMiddle East Technical UniversityAnkaraTurkey
  3. 3.Johann Radon Institute for Computational and Applied MathematicsAustrian Academy of SciencesLinzAustria
  4. 4.Department of Mathematics and Computer SciencesNecmettin Erbakan UniversityKonyaTurkey